How to plot all points that are defined by $(4\kappa+2(\lambda \mod 2), 2\lambda\sqrt 3)$ in Wolfram Alpha?

Question

How to plot all points that are defined by $(4\kappa+2(\lambda\mod2), \ 2\lambda\sqrt 3)$ for some $\kappa$ and $\lambda$ that are integers in Wolfram Alpha? I just want to know what this set of points looks like (I need it to understand a research paper). Thank you.

Answer 1

I would not use Wolfram|Alpha. Use a Wolfram Cloud Sandbox command similar to ListPlot[Table[{4 k + 2 Mod[n,2], 2 n Sqrt[3]}, {k,-3,3}, {n,-4,4}]]

The points form a Hexagonal lattice in the plane which determines a tiling by equilateral triangles.